Advertisements
Advertisements
प्रश्न
Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.
| Dividend | Divisor |
| 6y5 − 28y3 + 3y2 + 30y − 9 | 2y2 − 6 |
उत्तर
Quotient = \[3 y^3 - 5y + \frac{3}{2}\]
Remainder = 0
Divisor = 2y2 - 6
Divisor x Quotient + Remainder =
\[(2 y^2 - 6) \left( 3 y^3 - 5y + \frac{3}{2} \right) + 0\]
\[ = 6 y^5 - 10 y^3 + 3 y^2 - 18 y^3 + 30y - 9\]
\[ = 6 y^5 - 28 y^3 + 3 y^2 + 30y - 9\]
= Dividend
Thus, Divisor x Quotient + Remainder = Dividend
Hence verified.
APPEARS IN
संबंधित प्रश्न
Divide the given polynomial by the given monomial.
(5x2 − 6x) ÷ 3x
Divide the given polynomial by the given monomial.
(3y8 − 4y6 + 5y4) ÷ y4
Divide the given polynomial by the given monomial.
(p3q6 − p6q3) ÷ p3q3
Which of the following expressions are not polynomials?
Divide −4a3 + 4a2 + a by 2a.
Divide\[\sqrt{3} a^4 + 2\sqrt{3} a^3 + 3 a^2 - 6a\ \text{by}\ 3a\]
Divide 2y5 + 10y4 + 6y3 + y2 + 5y + 3 by 2y3 + 1.
Using division of polynomials, state whether
2x2 − x + 3 is a factor of 6x5 − x4 + 4x3 − 5x2 − x − 15
Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:
y4 + y2, y2 − 2
Divide:
(a2 + 2ab + b2) − (a2 + 2ac + c2) by 2a + b + c
